The Republicans have been the party of "whatever happened to the America I grew up in?" for close to 50 years, and probably more like 80 years. Thus, I think we can assume that the Republican Party of 2050 will be pining for the days when a "moderate" Democrat like Barack Obama could put aside partisanship and get good conservative policies like Obamacare and the repeal of DOMA through Congress.
I hear a lot more Democrats pining for the Republicans of old than vice versa. Democrats' favorite thing in the WORLD, regardless of time period or political climate, is to talk about how Republicans have gone crazy and how all past Republicans would be moderate Democrats today (reason: cuz!).